A vertex can represent
a person, object, location, or number
a variable or a pathway
a point, and nothing more

Answer: 14

Step-by-step explanation:

Given the sequence : 55 176 539 1628

Each number after the first is derived by multiplying by x and then adding y;

If x and y are > 0 and they are integers.

Taking 55 and 176:

176 = 55*x + y

539 = 176*x + y

55x + y = 176 - - - (1)

176x + y = 539 - - (2)

From (1) y = 176 - 55x

Substitute y = 176 - 55x into (2)

176x + 176 - 55x = 539

121x = 539 - 176

121x = 363

x = 363 / 121

x = 3

Put x = 3 in y = 176 - 55x

y = 176 - 55(3)

y = 176 - 165

y = 11

x = 3, y = 11

x + y = 3 + 11 = 14

Answer:

12.2 oz

Step-by-step explanation:

you would just plug in 2 for x so you get 0.6(2)+11 and which you simplify to get 1.2+11 and then you would get 12.2 as the weight

Answer: When combining like terms, add or subtract the coefficients. Keep the exponents as they are.

Step-by-step explanation:

You can combine 2x^2 + 3x^2 to get 5x^2. If x =3, 3^2=9 So 2(3)^2 is 18 and 3(3)^2 is 27. 18+27=45 And 5(3)^2= 45. Same result!

You can not combine 2x^2 and 2x^3. If the value of x is 3, 2(3)^2 this term works out to =18 and 2(3)^3 =54

If you add the exponents x^5 becomes 2(3)^5 or 2×243=486. Vastly different values! Don't add exponents unless you are multiplying terms.

Yes, when combining like terms with exponents, you add the exponents only if the terms have the same base.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

When combining like terms with exponents, you add the exponents only if the terms have the same base.

For example,

3x² + 9x²

= (3 + 9)x²

= 12x²

And,

2² x 2³

= [tex]2^{2 + 3}[/tex]

= [tex]2^5[/tex]

Thus,

Yes, we add the exponents.

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Step-by-step explanation:

Hey, there!!

Let me explain you very simply, ok.

Here, according to the question,

[tex]{x}^{2} = \frac{25}{144} [/tex]

X is square so, which finding the value of x you must take it to the right side (in root form ). so,

[tex]x = \sqrt{ \frac{25}{144} } [/tex]

Now, as we know that,

sq.root of 25 = 5

sq.root of 144 = 12

Now, you write it as,

[tex]x = \sqrt{ \frac{ {5}^{2} }{ {12}^{2} } } [/tex]

[tex]or \: x = \sqrt{( { \frac{5}{12} )}^{2} } [/tex]

Now, square root and (5/12) square ( square root , square gets cancelled).

You will get as,

[tex]x = \frac{5}{12} [/tex]

And its your simplified answer.

Hope it helps...

Answer:

1000m (option A)

Step-by-step explanation:

[tex]10^k^-^3 = m \\=>\frac{10^k}{10^3} = m \\=> 10^k = 1000 m[/tex]

Answer:

See below.

Step-by-step explanation:

So we have the parent function:

[tex]f(x)=x^2[/tex]

And it was transformed into:

[tex]g(x)=(3x)^2+6[/tex]

First, the +6 at the very end simply tells us that the graph was shifted upwards by 6 units.

For the (3x), this is essentially saying that:

[tex]f(x)=x^2[/tex]

If we use 3x for x:

[tex]f(3x)=(3x)^2[/tex]

Therefore, we essentially multiplied the x variable by 3.

In other words, this is a horizontal compression by a factor of 3.

So, our transformations are:

1) 6 units upwards

2) Horizontal compression by 3

Answer:

A

Step-by-step explanation:

The answer is A

Answer:

64 poles

Step-by-step explanation:

Given the question :

Fence posts are erected 5m apart (with a post at each corner) to support fencing round a rectangular field. If the field measures 100m by 60m, how many posts are needed?

Dimension of rectangular field = 100m by 60m

Length = 100m ; breadth = 60m

Since it is erected around the corners of the field, we need to calculate the entire perimeter of the rectangular field.

Perimeter of a rectangle : 2( length + breadth)

Perimeter = 2(100 +60) = 2(160) = 320m

Since the posts are erected 5m apart, the number of post needed will be :

Perimeter / 5

= 320 / 5

= 64 poles

Answer:

Step-by-step explanation:

[tex]\left(w^8\right)^8\\[/tex]

[tex]\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc}[/tex]

[tex]\left(w^8\right)^8=w^{8\times\:8}\\=w^6^4[/tex]

Answer:

(-1,-9) PLEASE MARK BRAINLIEST!!!!!

Step-by-step explanation:

k(-4,-6) , m(-7,-3)

-7+4=-3

-3+6=3

-4+3=-1

-6-3=-9

(-1,-9)

The coordinate of L is  (-1,-9) if the k is the midpoint of LM and k (-4,-6) and M (-7,-3).

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

It is given that:

if k is the midpoint of LM and k (-4,-6) and m(-7,-3).

It is required to find the coordinate of L:

Using the mid-point theorem:

Let the coordinate of L is (x, y)

(x - 7)/2 = -4

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.

x - 7 = -8

x = -8 + 7

x = -1

(y - 3)/2 = -6

y - 3 = -12

y = -12 + 3

y = -9

The coordinate of L is  (-1,-9)

Thus, the coordinate of L is  (-1,-9) if the k is the midpoint of LM and k (-4,-6) and M (-7,-3).

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Answer:

The elm tree is 40 5/6 inches tall

Step-by-step explanation:

Let

Tallness of the apple tree = x

Tallness of the elm tree= 3 1/2x

Apple tree = 10 2/3 feet tall

Elm tree = 3 1/2x

Where x= 10 2/3

Elm = 3 1/2 (10 2/3)

= 7/2(35/3)

= 7*35 / 2*3

= 245 / 6

= 40 5/6 inches tall

The elm tree is 40 5/6 inches tall

Answer:

x =-3

Step-by-step explanation:

1x + 2 = 0x + 5

hence 0x simplifies x

1x-0x = 2-5

x = -3

Answer:

77

Step-by-step explanation:

(6 + 3)² is same as (a +  b)²

Since (a +  b)² = a² + 2ab + b²

Therefore,

(6 + 3)² - 4

= (36 + 36 + 9) - 4

= 81 - 4

= 77  

Hi there! Hopefully this helps!

-------------------------------------------------------------------------------------------------------

Since PEMDAS exists, we will do parentheses "(6+3)" first to get 9.

Then we do the exponent which is:

[tex]9^{2}[/tex] = 81.

Then we subtract.

81 - 4 = 77.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

More broken down explanation:

[tex](6+3)^{2} -4[/tex]

Add 6 and 3 to get 9.

[tex]9^{2} - 4[/tex] ≈ [tex]77[/tex]

Calculate 9 to the power of 2 and get 81.

[tex]81-4[/tex] = [tex]77[/tex]

Answer:

  f(a) = 6a -5

Step-by-step explanation:

Assuming your function is ...

  f(x) = 6x -5

The expression f(a) means you replace x with 'a' everywhere in the above function definition:

  f(a) = 6a -5

Answer:

8

Step-by-step explanation:

3/5=0.6

32^0.6=8

Ans.8

Answer:

Two equal sides = 14.4 inches each

Shortest side = 7.2 inches

Step-by-step explanation:

a + b + c = 36

a = b

a = 2c

then:

c = a/2

a + a + a/2 = 36

2a + a/2 = 36

4a/2 + a/2 = 36

5a/2 = 36

a = 2*36/5

a = 72/5

a = 14.4

a = 2c

14.4 = 2*c

c = 14.4/2

c = 7.2

a = b

b = 14.4

Check:

14.4 + 14.4 + 7.2 = 36

Answer:

The radius, r₂, of the ball that uses one-half the amount of rubber coating used to cover the 16-inch ball is approximately 4.66 inches

Step-by-step explanation:

The dimension of the ball with known radius = 16-inch

The surface area of the ball with 16-inch radius = 4×π×r² = π·D² = π×16² = 804.24772 in.²

Given that the ball uses one-half the rubber material coating used to cover the 16-inch ball, we have the surface area of the ball = 804.24772 in.²/2 = 402.12386 in.²

The radius, r₂ of the new ball is found as follows;

402.12386 in.² = 4×π×r₂²

r₂² = 402.12386 in.² /(4×π) ≈ 32

r₂ = √32 = 4·√2 ≈ 4.66 inches

The radius, r₂, of the ball that uses one-half the amount of rubber coating used to cover the 16-inch ball ≈ 4.66 inches.

Answer:

Step-by-step explanation:

We are going to assume that the cylinder is filled with water to the brim

Given that the data of the cylinder is

height h= 180 cm

radius r= 60 cm

The formula for the volume of a cylinder is

[tex]volume= \pi r^2h[/tex]

[tex]volume = 3.142*60^2*180\\\\volume= 3.142*3600*180\\\\volume= 20360.16 cm^3[/tex]

The volume of water in the cylinder is 20360.16 cm^3

Answer:

66.6% (see below)

Step-by-step explanation:

Each sphere 4/3[tex]\pi[/tex]r²=4/3[tex]\pi[/tex](4²)=268.08cm³

Assuming the tube is the same width and height as the three spheres,

V=[tex]\pi[/tex]r²h=[tex]\pi[/tex](4²)24=1206.37

The three spheres are 268.08*3=804.24cm³

The tube is 1206.37cm³

I’m not sure if your question is asking the percentage of the tube that’s filled, or the percentage that’s unfilled.

Filled: 804.24÷1206.37=0.66666=66.6%

Unfilled: 1206.37-804.24=402.13

402.13÷106.37=0.33333=33.3%

Answer:

Percentage of Tube Unfilled : 33 and 1/3%

Step-by-step explanation:

It's most likely that we want to calculate the percentage of the tube unfilled, as the tube itself wouldn't be provided otherwise. We can start by calculating the volume of the tube --- (1)

The volume of a cylinder is represented by πr²h. Substituting we would receive π(4)²h. h is represented by 3 times the diameter of each sphere, as it is aligned such. Diameter = 2 * r = 2 * 4 = 8, so h = 3 * 8 = 24. Therefore Tube Volume = π(4)²(24) = π(16)(24) = 384π.

Now let's solve for the volume of a sphere, multiplying by three to receive the total volume of all 3 spheres --- (2)

Volume of 1 Sphere : 4 / 3πr³ = 4 / 3π(4)³ = 4 / 3π * 64 = 256 / 3π

Volume of all 3 Spheres : 256 / 3π * 3 = 256π

And now the volume of the tube that is unfilled, will be 384π - 256π = 128π. The total volume of the tube is 384π, so the percentage of the unfilled tube will be 128π / 384π or 128 / 384 = 0.333333333 * 100 = 33.33333...%. Therefore the percentage of the tube that is not filled will be 33.33% approximately, or 33 and 1/3% in exact terms.

Answer:

[tex]x = \frac{w}{(u + r)} [/tex]

Step-by-step explanation:

ux + rx = w

x(u + r) = w

x = w/(u + r)

the dash '/' represents fraction

The required solution is x = w/(u + r).

It is required to find the value of x.

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given:

The given equation is

u x + r x = w

Taking common x  we get,

x(u + r) = w

Divide (u + r)  on both sides we get,

x = w/(u + r)

Therefore, the required solution is x = w/(u + r).

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The expression that shows the total number of songs on Iris playlist is 120 + 4w

A linear expression is an expression that has only one variable. The single variable is raised to the power of 1.  An example of a linear expression is x + 10  

Iris already has 120 songs on her playlist. She increases her playlist every week by four songs.

This means that each week, her playlist increases by 4. This can be represented with the expression : 4 x w = 4w

Where w represents the number of weeks.

In week 10, her playlist increases by: 4 x 1 = 4 songs

In week 10, her playlist increases by : 4 x 10 = 40 songs

But Iris already has 120 songs

This can be represented with the expression 120 + 4w

After 1 week, the total songs she would have is 120 + 4 = 124 songs

After 10 weeks, the total songs she would have is 120 + 40 = 160 songs

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Answer:

The range can be expressed as: [tex]30.485\leq x\leq 30.515[/tex]

which agrees with answer D

Step-by-step explanation:

If the tolerance is 0.015 cm for the final rod, then the range of acceptable lengths for the rod is between 30.5 - 0.05 and 30.5 + 0.015 . That is between

30.485 cm and 30.515 cm

Which can be expressed as:   [tex]30.485\leq x\leq 30.515[/tex]

Answer:

He gets less buying the two big bags

Step-by-step explanation:

Answer:

(5x-2)

Step-by-step explanation:

first factor the quadratic equation

10x²+26x-12 by factoring out the gcf of 2

2(5x²+13x-6)    to factor the quadratic, first multiply ac (5)(-6)

find factors of -30 that multiply to give you -30 and add to give you the middle term 13.

factors -2, 15

take your leading term 5x and put it over the 2 factors, then reduce when necessary.  it is not necessary to use the 5x² because the x in the denominator cancels one out)

5x/-2 and 5x/15 (this one can be reduced to x/3

(5x-2)(x+3) are the factors.

the shared factor is (5x-2)

Answer:

they share 5x-2 as common factor

Step-by-step explanation:

10x² + 26x – 12 and 2(5x – 2)(x – 3)

10x² + 26x – 12  take 2 as common factor

2(5x²+13x-6)     factorize

2(5x-2)(x+3)

they share 5x-2 as common factor

Answer:

24 : 84 = 2 : 7

Step-by-step explanation:

We can simplify the ratio 24 : 84 by dividing both terms by the greatest common factor (GCF).

The GCF of 24 and 84 is 12.

Divide both terms by 12.

24 ÷ 12 = 2

84 ÷ 12 = 7

Therefore:

24 : 84 = 2 : 7

Answer:

Step-by-step explanation:

(x + 2)/2 = -2

x + 2 = -4

x = -6

(y + (-9))/2 = -1

y - 9 = -2

y = 7

(-6, 7)

answer is C

Answer: (5 + 2x)(5 - 2x)

Step-by-step explanation:

It seems a bit backwards from the way these are usually set up, but still it is the difference of two perfect squares.

Answer:

.6x - 4 = .83

Step-by-step explanation:

Answer:

Ezequiel's final grade is 8

Step-by-step explanation:

The average (mean) of Ezequiel's grade is:

[tex]\frac{(8.3+6.8+9.4)}{3} \approx 8.16666[/tex]

which rounded to the nearest unit is 8.

Answer:

It would be 8 :)

Step-by-step explanation: